The document discusses properties of regular polygons, including the number of sides, total interior angle, and ability to tessellate. It notes that triangles, squares, and hexagons can tessellate because the sum of their interior angles is 360 degrees. Pentagons and octagons cannot tessellate as their interior angles sum to less than 360 degrees. Examples of tessellation patterns using triangles, squares, and hexagons are also provided.
This document discusses properties of polygons, including:
1) The sum of interior angles in a triangle is 180 degrees, and the sum of interior angles in an n-sided polygon is (n-2) x 180 degrees.
2) The sum of angles can be 900 degrees for a heptagon/septagon with 7 sides, but cannot be 1600 degrees as that number of degrees does not correspond to a whole number of sides.
3) The sum of outer angles (exterior angles) of any polygon is always 360 degrees, with the outer angles at each vertex summing to 180 degrees.
The document provides steps to calculate the interior angles of a regular polygon. It states that for a regular polygon with n sides, take n - 2 and multiply it by 180 degrees to get the total interior angle measurement. For a hexagon with 6 sides, take 6 - 2 which is 4, and multiply 4 by 180 to get 720 degrees as the total interior angle measurement.
The document describes how to draw angles in standard position on a unit circle and convert between degrees and radians. It provides examples of drawing angles such as 210°, -45°, and 540° in standard position and rewriting angles such as 30°, 45°, and an unspecified angle in radians and degrees. It also gives examples of finding coterminal angles for 210° with one positive and one negative measure.
The document outlines 16 steps to develop a hexagonal pyramid with a hole from its front, top, and side views. It involves drawing the base and hole, identifying cut edges, finding true lengths, plotting edges on an arc representing the slant height, and transferring cutting points and edges to the unfolded development. Careful naming and measuring is required to avoid errors in the developed figure. Additional practice is recommended to fully understand the process.
This document provides information about polygons for a student named Dilna M Raju enrolled in a B.Ed. Mathematics program from 2018-2020. It defines polygons as closed figures with three or more sides and provides properties of polygons, including that the sum of angles in an n-sided polygon is (n-2)×180 degrees, the sum of outer angles is 360 degrees, and a regular polygon has equal sides and angles.
The document is about regular polygons and their properties. It defines regular polygons as closed figures with equal sides and equal interior angles. It provides examples of regular polygons like triangles, squares, pentagons and hexagons. It gives the formula to find the sum of interior angles of a regular polygon as (n-2)180, where n is the number of sides. As an example, it calculates the sum of interior angles of an octagon as 6*180 = 1080. It also proves that the sum of outer angles of any n-sided polygon is always 360.
Chapter 2 polygons ii [compatibility mode]Khusaini Majid
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The document discusses properties of regular and irregular polygons, including:
- A regular polygon has equal side lengths and interior angles, while an irregular polygon does not.
- The interior angle plus exterior angle of any polygon equals 180 degrees.
- The sum of the exterior angles of any polygon is 360 degrees.
- The sum of the interior angles of an n-sided polygon is (n - 2) × 180 degrees.
- For a regular polygon, the interior angle is (n - 2) × 180/n degrees and the exterior angle is 360/n degrees.
This document provides information about angle facts and properties. It defines key angle terms such as acute, obtuse, right, reflex, perpendicular, and parallel lines. It describes properties of angles including: angles at a point sum to 360 degrees; opposite angles are equal; corresponding angles are equal for parallel lines with a transversal; alternate angles are equal; and interior angles sum to 180 degrees. Examples are provided to demonstrate how to use these properties to determine unknown angle measures.
The document discusses properties of regular polygons, including the number of sides, total interior angle, and their ability to tessellate. Regular polygons that can tessellate are those where the sum of the interior angles equals 360 degrees. Specifically, triangles, squares, and hexagons tessellate, while pentagons and octagons do not tessellate because their interior angle sums are less than 360 degrees. Examples of tessellation patterns involving triangles, squares, hexagons and octagons are provided.
The document discusses properties of regular polygons, including the number of sides, total interior angle, and ability to tessellate. It notes that triangles, squares, and hexagons can tessellate because the sum of their interior angles is 360 degrees. Pentagons and octagons cannot tessellate as their interior angles sum to less than 360 degrees. Examples of tessellation patterns using triangles, squares, and hexagons are also provided.
This document provides information about polygons, including definitions, classifications, names of polygons based on number of sides, properties of interior and exterior angles, and formulas to calculate sums and measures of angles. It defines a polygon as a closed figure formed by line segments that intersect only at endpoints. Polygons are classified as regular, irregular, convex, or concave. Common polygon names are provided for up to 12 sides. Formulas are given for calculating the sum of interior and exterior angles based on the number of sides of the polygon.
There are four types of angles: acute, obtuse, right and reflex. Angle properties include: angles at a point add to 360 degrees; angles on a straight line add to 180 degrees; vertically opposite angles are equal; corresponding angles and alternate interior angles of parallel lines are equal; interior angles of a triangle add to 180 degrees; exterior angle of a triangle equals the sum of the interior opposite angles; interior angles of polygons add up based on the number of sides, following the formula (n-2) x 180 degrees, where n is the number of sides. Regular polygons have equal interior angles that add up to the total interior angle based on the number of sides.
The document discusses different types of polygons and their properties. It defines concave and convex polygons, interior and exterior angles, and provides a formula to calculate the sum of interior angles based on the number of sides. It also discusses regular polygons and how the sum of exterior angles is always 360 degrees for convex polygons.
This document discusses different types of angles:
- Right angles measure 90 degrees
- Acute angles measure less than 90 degrees
- Obtuse angles measure more than 90 degrees but less than 180 degrees
- Straight angles measure 180 degrees
- Reflex angles measure more than 180 degrees
It provides examples of estimating and comparing different angle types, and includes activities to identify angle types in real world examples and practice calculating missing angles.
The document discusses polygons and their properties. It defines polygons as closed, plane figures with three or more sides. It discusses regular polygons which have congruent sides and angles. It provides the formula to find the sum of interior angles of any polygon as 180(n-2) where n is the number of sides. It gives examples of finding sums and measures of interior angles for different polygons like triangles, quadrilaterals, pentagons using the formula. Special types of quadrilaterals with additional properties are also defined.
The document discusses polygons and their properties. It defines polygons as closed, plane figures with three or more sides. It discusses regular polygons which have congruent sides and angles. It provides the formula to find the sum of interior angles of any polygon as 180(n-2) where n is the number of sides. It gives examples of finding sums and measures of interior angles for different polygons like triangles, quadrilaterals, pentagons using the formula. Special types of quadrilaterals with additional properties are also defined.
This document provides reminders of several geometric rules for determining unknown angle measures, including that angles in a straight line equal 180 degrees, angles in a triangle equal 180 degrees, interior angles of a quadrilateral equal 360 degrees, vertically opposite angles are equal, corresponding angles are equal, and alternate angles are equal. Examples are given applying each rule to solve for unknown angle measures.
This document provides an overview of key concepts related to lines, angles, and shapes in geometry:
1. It defines lines, line segments, and angles, and explains how they are labeled.
2. It describes parallel and perpendicular lines, and explores properties like corresponding angles.
3. It covers calculating and classifying angles, such as complementary, supplementary, and vertically opposite angles.
4. It examines angles in triangles and quadrilaterals, noting the sums of interior and exterior angles.
The document discusses different types of triangles: isosceles triangles which have two equal sides and angles, equilateral triangles which have three equal sides and angles of 60 degrees each, and right triangles which have one 90 degree angle. It explains that the sum of the interior angles of any triangle is always 180 degrees, and uses this property to calculate unknown angles. It also defines congruent triangles as those with identical angles and side lengths.
This document defines and provides examples of different types of polygons. It explains that a polygon is a closed figure made of line segments that intersect exactly two others. It then defines regular and irregular polygons, as well as different types of triangles, quadrilaterals, pentagons, hexagons, and other polygons. Key details like the number of sides and sum of interior angles are provided. Examples of both regular and irregular shapes are shown.
This document discusses properties of regular polygons. It states that a regular polygon has all sides of equal length and all interior angles of equal size. The number of axes of symmetry equals the number of sides. The interior and exterior angles at each vertex sum to 180 degrees. Formulas are provided for calculating the sum of interior angles, the measure of each interior angle, the sum of exterior angles, and the measure of each exterior angle of a regular n-polygon.
This document defines and explains different types of angles and angle relationships, including:
- Acute, right, obtuse, and straight angles
- Parallel and perpendicular lines
- Vertical, corresponding, alternate interior, alternate exterior, and consecutive interior angles
- Complementary, supplementary, and adjacent angles
Worked examples are provided to demonstrate finding missing angle measures using properties of these angles and angle relationships.
This document discusses angles in polygons. It defines regular and irregular polygons, and provides examples of polygon names for different numbers of sides. The document also discusses calculating unknown angles, finding interior and exterior angles, and the relationship between the number of sides and sum of interior angles for different polygons. Examples are provided to demonstrate calculating unknown angles in polygons and finding the type of triangle based on given angle measures.
Multiplying using the table or box method keithpeter
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This alternative method of doing long multiplication helps to separate the multiplying from the adding. The method also gives greater insight into what long multiplication is, and helps lay a foundation for algebra 'FOIL' later.
This document provides information about angle facts and properties. It defines key angle terms such as acute, obtuse, right, reflex, perpendicular, and parallel lines. It describes properties of angles including: angles at a point sum to 360 degrees; opposite angles are equal; corresponding angles are equal for parallel lines with a transversal; alternate angles are equal; and interior angles sum to 180 degrees. Examples are provided to demonstrate how to use these properties to determine unknown angle measures.
The document discusses properties of regular polygons, including the number of sides, total interior angle, and their ability to tessellate. Regular polygons that can tessellate are those where the sum of the interior angles equals 360 degrees. Specifically, triangles, squares, and hexagons tessellate, while pentagons and octagons do not tessellate because their interior angle sums are less than 360 degrees. Examples of tessellation patterns involving triangles, squares, hexagons and octagons are provided.
The document discusses properties of regular polygons, including the number of sides, total interior angle, and ability to tessellate. It notes that triangles, squares, and hexagons can tessellate because the sum of their interior angles is 360 degrees. Pentagons and octagons cannot tessellate as their interior angles sum to less than 360 degrees. Examples of tessellation patterns using triangles, squares, and hexagons are also provided.
This document provides information about polygons, including definitions, classifications, names of polygons based on number of sides, properties of interior and exterior angles, and formulas to calculate sums and measures of angles. It defines a polygon as a closed figure formed by line segments that intersect only at endpoints. Polygons are classified as regular, irregular, convex, or concave. Common polygon names are provided for up to 12 sides. Formulas are given for calculating the sum of interior and exterior angles based on the number of sides of the polygon.
There are four types of angles: acute, obtuse, right and reflex. Angle properties include: angles at a point add to 360 degrees; angles on a straight line add to 180 degrees; vertically opposite angles are equal; corresponding angles and alternate interior angles of parallel lines are equal; interior angles of a triangle add to 180 degrees; exterior angle of a triangle equals the sum of the interior opposite angles; interior angles of polygons add up based on the number of sides, following the formula (n-2) x 180 degrees, where n is the number of sides. Regular polygons have equal interior angles that add up to the total interior angle based on the number of sides.
The document discusses different types of polygons and their properties. It defines concave and convex polygons, interior and exterior angles, and provides a formula to calculate the sum of interior angles based on the number of sides. It also discusses regular polygons and how the sum of exterior angles is always 360 degrees for convex polygons.
This document discusses different types of angles:
- Right angles measure 90 degrees
- Acute angles measure less than 90 degrees
- Obtuse angles measure more than 90 degrees but less than 180 degrees
- Straight angles measure 180 degrees
- Reflex angles measure more than 180 degrees
It provides examples of estimating and comparing different angle types, and includes activities to identify angle types in real world examples and practice calculating missing angles.
The document discusses polygons and their properties. It defines polygons as closed, plane figures with three or more sides. It discusses regular polygons which have congruent sides and angles. It provides the formula to find the sum of interior angles of any polygon as 180(n-2) where n is the number of sides. It gives examples of finding sums and measures of interior angles for different polygons like triangles, quadrilaterals, pentagons using the formula. Special types of quadrilaterals with additional properties are also defined.
The document discusses polygons and their properties. It defines polygons as closed, plane figures with three or more sides. It discusses regular polygons which have congruent sides and angles. It provides the formula to find the sum of interior angles of any polygon as 180(n-2) where n is the number of sides. It gives examples of finding sums and measures of interior angles for different polygons like triangles, quadrilaterals, pentagons using the formula. Special types of quadrilaterals with additional properties are also defined.
This document provides reminders of several geometric rules for determining unknown angle measures, including that angles in a straight line equal 180 degrees, angles in a triangle equal 180 degrees, interior angles of a quadrilateral equal 360 degrees, vertically opposite angles are equal, corresponding angles are equal, and alternate angles are equal. Examples are given applying each rule to solve for unknown angle measures.
This document provides an overview of key concepts related to lines, angles, and shapes in geometry:
1. It defines lines, line segments, and angles, and explains how they are labeled.
2. It describes parallel and perpendicular lines, and explores properties like corresponding angles.
3. It covers calculating and classifying angles, such as complementary, supplementary, and vertically opposite angles.
4. It examines angles in triangles and quadrilaterals, noting the sums of interior and exterior angles.
The document discusses different types of triangles: isosceles triangles which have two equal sides and angles, equilateral triangles which have three equal sides and angles of 60 degrees each, and right triangles which have one 90 degree angle. It explains that the sum of the interior angles of any triangle is always 180 degrees, and uses this property to calculate unknown angles. It also defines congruent triangles as those with identical angles and side lengths.
This document defines and provides examples of different types of polygons. It explains that a polygon is a closed figure made of line segments that intersect exactly two others. It then defines regular and irregular polygons, as well as different types of triangles, quadrilaterals, pentagons, hexagons, and other polygons. Key details like the number of sides and sum of interior angles are provided. Examples of both regular and irregular shapes are shown.
This document discusses properties of regular polygons. It states that a regular polygon has all sides of equal length and all interior angles of equal size. The number of axes of symmetry equals the number of sides. The interior and exterior angles at each vertex sum to 180 degrees. Formulas are provided for calculating the sum of interior angles, the measure of each interior angle, the sum of exterior angles, and the measure of each exterior angle of a regular n-polygon.
This document defines and explains different types of angles and angle relationships, including:
- Acute, right, obtuse, and straight angles
- Parallel and perpendicular lines
- Vertical, corresponding, alternate interior, alternate exterior, and consecutive interior angles
- Complementary, supplementary, and adjacent angles
Worked examples are provided to demonstrate finding missing angle measures using properties of these angles and angle relationships.
This document discusses angles in polygons. It defines regular and irregular polygons, and provides examples of polygon names for different numbers of sides. The document also discusses calculating unknown angles, finding interior and exterior angles, and the relationship between the number of sides and sum of interior angles for different polygons. Examples are provided to demonstrate calculating unknown angles in polygons and finding the type of triangle based on given angle measures.
Multiplying using the table or box method keithpeter
Ìý
This alternative method of doing long multiplication helps to separate the multiplying from the adding. The method also gives greater insight into what long multiplication is, and helps lay a foundation for algebra 'FOIL' later.
Scatter diagrams, strong and weak correlation, positive and negative correlation, lines of best fit, extrapolation and interpolation. Aimed at UK level 2 students on Access and GCSE Maths courses.
Scatter diagrams, strong and weak correlation, positive and negative correlation, lines of best fit, extrapolation and interpolation. Aimed at UK level 2 students on Access and GCSE Maths courses.
Demonstration of cancelling down a fraction to its lowest terms. Single step examples using the 3 and 7 times table. How to cancel fractions with larger numbers in several steps. How to use the prime factors of the numerator and denominator to cancel large fractions.
This document discusses three domains - filing cabinet, tutor lead, and student driven - that can be used to classify Moodle courses. It suggests imagining scoring courses based on the percentage they use each domain. Filing cabinet courses primarily provide access to learning materials, tutor lead courses feature quizzes and forums led by instructors, and student driven courses emphasize reflection and independent student activity. An effective course design depends on the goals of the course and may polarize towards one domain rather than taking a balanced approach.
Algebra, level 2 in the UK system. One pdf slide with an A4 format handout that summarises collecting terms, multiplying terms, cancelling algebraic fractions, multiplying out brackets.
This slide show covers adding two fractions with the same denominator, adding two fractions with one denominator that is a factor of the other, and, finally adding fractions with different denominators. There are a small number of questions for a class to complete as a 'check on learning' during the presentation. I'm assuming the class have access to a textbook or other collection of problems for use after the presentation.
This slideshare version is pretty dry. I usually include a visual 'starter' image of some kind, often a funny sign or joke or screen grab of a news article.
This powerpoint with a number of examples of each topic lasted for a 1.5 hour lesson.Plenty of practical graph drawing. Some of the custom builds don't work on slideshare
This document provides an introduction to probability and statistics concepts. It discusses probability basics like expected frequency and experimental probability. It also covers topics like tree diagrams, mutually exclusive and independent events, and how to calculate probabilities of combined outcomes using multiplication and addition. Sample probability questions are provided relating to coins, dice, and colored balls to illustrate these concepts.
GCSE Maths reverse percentages questions using a ruler and the length of shapes. I\'m trying this approach to see if I can cut out some of the verbal issues that arise in \'story problems\'
Ratios illustrated: dividing in a ratio and calculating the value of one part (or the whole) given the value of another part. GCSE Maths and Level 2 Maths.
A blog is a website where journal-style entries are posted in reverse chronological order. Blogs can be used to provide commentary on various topics or function as personal online diaries. They typically contain text, images, and links. Readers can leave interactive comments.
Blogging for teachers has benefits - it allows easy publication and reading of content. Setting up a blog is straightforward using platforms like Blogger. Teachers should blog regularly to share knowledge and get recognized for their expertise, which can help their institution. However, blogs should further educational goals rather than being an outlet for personal issues.
A blog is a website where journal-style entries are posted in reverse chronological order. Blogs often provide commentary on a particular topic and allow readers to leave interactive comments. Setting up a blog through Blogger is easy and free, requiring only an email address and choosing a blog name and subdomain. Blogs are useful for teachers to share resources with students, build links over time, and get recognized for their expertise in a particular area.
This short document discusses staff development, finding employees, accidental learning, and the future in 4 brief questions. It poses questions about the amount of staff development that occurs, if it is a good place to find people, the role of accidental learning, and thoughts on the future.
Prelims of Rass MELAI : a Music, Entertainment, Literature, Arts and Internet Culture Quiz organized by Conquiztadors, the Quiz society of Sri Venkateswara College under their annual quizzing fest El Dorado 2025.
The Constitution, Government and Law making bodies .saanidhyapatel09
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This PowerPoint presentation provides an insightful overview of the Constitution, covering its key principles, features, and significance. It explains the fundamental rights, duties, structure of government, and the importance of constitutional law in governance. Ideal for students, educators, and anyone interested in understanding the foundation of a nation’s legal framework.
APM People Interest Network Conference 2025
-Autonomy, Teams and Tension: Projects under stress
-Tim Lyons
-The neurological levels of
team-working: Harmony and tensions
With a background in projects spanning more than 40 years, Tim Lyons specialised in the delivery of large, complex, multi-disciplinary programmes for clients including Crossrail, Network Rail, ExxonMobil, Siemens and in patent development. His first career was in broadcasting, where he designed and built commercial radio station studios in Manchester, Cardiff and Bristol, also working as a presenter and programme producer. Tim now writes and presents extensively on matters relating to the human and neurological aspects of projects, including communication, ethics and coaching. He holds a Master’s degree in NLP, is an NLP Master Practitioner and International Coach. He is the Deputy Lead for APM’s People Interest Network.
Session | The Neurological Levels of Team-working: Harmony and Tensions
Understanding how teams really work at conscious and unconscious levels is critical to a harmonious workplace. This session uncovers what those levels are, how to use them to detect and avoid tensions and how to smooth the management of change by checking you have considered all of them.
Mate, a short story by Kate Grenvile.pptxLiny Jenifer
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A powerpoint presentation on the short story Mate by Kate Greenville. This presentation provides information on Kate Greenville, a character list, plot summary and critical analysis of the short story.
Digital Tools with AI for e-Content Development.pptxDr. Sarita Anand
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This ppt is useful for not only for B.Ed., M.Ed., M.A. (Education) or any other PG level students or Ph.D. scholars but also for the school, college and university teachers who are interested to prepare an e-content with AI for their students and others.
Research & Research Methods: Basic Concepts and Types.pptxDr. Sarita Anand
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This ppt has been made for the students pursuing PG in social science and humanities like M.Ed., M.A. (Education), Ph.D. Scholars. It will be also beneficial for the teachers and other faculty members interested in research and teaching research concepts.
How to attach file using upload button Odoo 18Celine George
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In this slide, we’ll discuss on how to attach file using upload button Odoo 18. Odoo features a dedicated model, 'ir.attachments,' designed for storing attachments submitted by end users. We can see the process of utilizing the 'ir.attachments' model to enable file uploads through web forms in this slide.
Finals of Kaun TALHA : a Travel, Architecture, Lifestyle, Heritage and Activism quiz, organized by Conquiztadors, the Quiz society of Sri Venkateswara College under their annual quizzing fest El Dorado 2025.
SOCIAL CHANGE(a change in the institutional and normative structure of societ...DrNidhiAgarwal
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This PPT is showing the effect of social changes in human life and it is very understandable to the students with easy language.in this contents are Itroduction, definition,Factors affecting social changes ,Main technological factors, Social change and stress , what is eustress and how social changes give impact of the human's life.
Database population in Odoo 18 - Odoo slidesCeline George
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In this slide, we’ll discuss the database population in Odoo 18. In Odoo, performance analysis of the source code is more important. Database population is one of the methods used to analyze the performance of our code.